Randomized Tensor Ring Decomposition and Its Application to Large-scale Data Reconstruction

Dimensionality reduction is an essential technique for multi-way large-scale data, i.e., tensor. Tensor ring (TR) decomposition has become popular due to its high representation ability and flexibility. However, the traditional TR decomposition algorithms suffer from high computational cost when facing large-scale data. In this paper, taking advantages of the recently proposed tensor random projection method, we propose two TR decomposition algorithms. By employing random projection on every mode of the large-scale tensor, the TR decomposition can be processed at a much smaller scale. The simulation experiment shows that the proposed algorithms are $4-25$ times faster than traditional algorithms without loss of accuracy, and our algorithms show superior performance in deep learning dataset compression and hyperspectral image reconstruction experiments compared to other randomized algorithms.Comment: ICASSP submissio

Block-Randomized Gradient Descent Methods with Importance Sampling for CP Tensor Decomposition

This work considers the problem of computing the CANDECOMP/PARAFAC (CP) decomposition of large tensors. One popular way is to translate the problem into a sequence of overdetermined least squares subproblems with Khatri-Rao product (KRP) structure. In this work, for tensor with different levels of importance in each fiber, combining stochastic optimization with randomized sampling, we present a mini-batch stochastic gradient descent algorithm with importance sampling for those special least squares subproblems. Four different sampling strategies are provided. They can avoid forming the full KRP or corresponding probabilities and sample the desired fibers from the original tensor directly. Moreover, a more practical algorithm with adaptive step size is also given. For the proposed algorithms, we present their convergence properties and numerical performance. The results on synthetic data show that our algorithms outperform the existing algorithms in terms of accuracy or the number of iterations